Question

The lengths of the sides of a triangle are in the extended ratio 4 ​: 7 ​: 8. The perimeter of the triangle is 95 cm. What are the lengths of the​ sides?

Answer 1

20 cm, 35 cm, 40 cm

Explanation:

sum the parts of the ratio, 4 + 7 + 8 = 19 parts

Divide the perimeter by 19 to find the value of one part of the ratio.

95 cm ÷ 19 = 5 cm, then

4 parts = 4 × 5 cm = 20 cm

7 parts = 7 × 5 cm = 35 cm

8 parts = 8 × 5 cm = 40 cm

Thus the 3 sides are 20 cm, 35 cm and 40 cm

Answer 2

The measure of the sides of a triangle will be:

4x = 4(5) = 20 cm

7x = 7(5) = 35 cm

8x = 8(5) = 40 cm

Explanation:

Given that the lengths of the sides of a triangle are in the extended ratio 4 ​: 7 ​: 8.

Also given that the perimeter of the triangle is 95 cm.

We know that the Perimeter of a triangle is the sum of all the sides of a triangle.

As the lengths of the sides of a triangle are in the proportion 4 ​: 7 ​: 8. Thus, the measure of the sides will have the same scale factor x.

Therefore,

4x + 7x + 8x = 95

Add similar elements: 4x + 7x + 8x = 19x

19x = 95

Divide both sides by 19

19x/19 = 95/19

x = 5

Therefore, the measure of the sides of a triangle will be:

4x = 4(5) = 20 cm

7x = 7(5) = 35 cm

8x = 8(5) = 40 cm

Verification:

20 + 35 + 40 = 95

95 = 95